Heuristic for using LMMs as a two-step process. This helps me conceptualise the process.

How to?

The two steps are: 1) determine whether the slopes of your effects differ, 2) test your main effects.

In order to do 1):

• Build the more complex (maximal) model.
• Check convergence with a large number of iterations.
• Build a reduced model by removing 1 element.
• Compare models in descending order: if there is a significant reduction in fit, accept the more complex model; if there is no decrease, continue descending.
• If further descending is needed, remove 1 element from the previously reduced model and repeat the process.
• Continue until a significant reduction in fit is found.
• Pro tip: the suggested reduction order is interactions > main effects.

In order to do 2), you can use a Chi-square likelihood ratio test. In R, this is what anova(reduced_model, full_model) does (not summary(), which only prints the coefficient estimates).

Pro tip: if you’re running a logistic (binomial) mixed model, you can get the effect size as an odds ratio by exponentiating the beta estimate — in R, exp() will do it for you. This only applies to logistic/binomial models; for a standard linear mixed model with a continuous outcome, the beta is already on the outcome’s scale and there’s no odds ratio to compute.